The Atangana-Baleanu fractional derivative in the Caputo sense (ABC) is
defined as (cf. [1]}):
\({}^{ABC}_{\quad \,0}D^{\alpha }_{t}f(t)=\displaystyle \frac{AB(\alpha )}{1-\alpha }\int ^{t}_{0}f^\prime (s)\textbf {E}_{\alpha }\left(\frac{-\alpha }{1-\alpha }(t-s)^{\alpha }\right) ds,\) 
